The 45-year-old faces an uncertain future at San Siro, having failed to guarantee a Champions League place before the final day of the season, on which ambitious Fiorentina can snatch third spot should Milan slip up at Siena.
Roma, who visited Milan for a controversial goalless draw on Sunday, are looking for a new coach following the departure of Zdenek Zeman in February.
But, in response to newspaper reports suggesting Allegri is ready to replace interim boss Aurelio Andreazzoli at the Stadio Olimpico, Milan issued a flat denial on behalf of their coach.
A statement published on acmilan.com read: "Massimiliano Allegri has denied meeting any representative from AS Roma as was reported in the media this morning."
The league meeting in Milan on Sunday was marred by racist chanting from a section of Roma fans, leading to a two-minute suspension in play, with the capital club subsequently receiving a 50,000 euro fine and an official warning over the future conduct of their supporters.
Rossoneri midfielder Sulley Muntari was earlier dismissed for physically restraining referee Gianluca Rocchi as he attempted to book the Ghanaian, while Roma captain Francesco Totti saw red late on for elbowing Philippe Mexes.